Don't both those chips, the AU and the MU, have similar dimensions, with the exception of the leg configuration
No, they don't. The standard TQFP package is 6.95mm square, the VQFN leadless is 3.95mm square, not quite half the size. Beware that some of the black boards have the FTDI connection points reversed, you have to flip your adapter over to flash them.
The nice thing about them is they use a real quartz crystal rather than a ceramic resonator so the clock source is more accurate over time and temperature, if that matters to you. The crystal is that big metal can next to the reset switch. In that ancient HC49/U package thru-lead package, it's bigger than the processor. But, hey, they're cheap.
Edit: what the ad should say is “replace ATmega168”, the 128 is a typical Chinese typo.